Majorana states in helical Shiba chains and ladders

TL;DR

This paper investigates the emergence and properties of Majorana bound states in various magnetic chain and ladder structures on superconductors, revealing new topological phenomena and conditions for their existence.

Contribution

It introduces a general criterion for Majorana edge states in multichain ladders and explores how magnetic domain walls and chain coupling affect topological states.

Findings

Domain walls support two Majorana states with enhanced conductance.

Coupled chains show nontrivial topological behavior beyond simple parity effects.

Ladders can host Majorana states even when individual chains are trivial.

Abstract

Motivated by recent proposals to realize Majorana bound states in chains and arrays of magnetic atoms deposited on top of a superconductor, we study the topological properties of various chain structures, ladders and two-dimensional arrangements exhibiting magnetic helices. We show that magnetic domain walls where the chirality of a magnetic helix is inverted support two protected Majorana states giving rise to a tunneling conductance peak twice the height of a single Majorana state. The topological properties of coupled chains exhibit nontrivial behaviour as a function of the number of chains beyond the even-odd dichotomy expected from the simple $\mathbb{Z}_2$ nature of coupled Majorana states. In addition, it is possible that a ladder of two or more coupled chains exhibit Majorana edge states even when decoupled chains are trivial. We formulate a general criterion for the number of Majorana edge states in multichain ladders and discuss some experimental consequences of our findings.